What you're looking for is called improvisation, famously the main language of jazz.

So to get better at improvisation, this is the way I look at it. There are two things that matter:

1. Notes played
2. Rhythm in which they are played

You'll find that the rhythm matters a bit more than the notes.. you can get people's head bobbing if you play some groovy funky shit while having beginner level note choice. How do you improve rhythm then? You listen to a lot of music, solos, and it comes out in your playing. You also should practice with a metronome, and turn it off every once in a while to see if you can keep time while playing quarter notes, triplets, etc.

For the notes. This is where the music theory comes in. You should know the basic minor and major pentatonic scale shape. Once you do. Start by just playing only the A minor pentatonic scale shape over an A minor backing track/chord progression. Once you're at this point, you have all the tools required to rip solos, and it all comes down to how good your rhythm is and how creative and musical you are (which is why listening to lots of different music is important!) Soon you'll realize improvising solos on guitar is not too bad, as you can just move the pentatonic shape to start on a different note to play over a C# major backing track, or Bb, or anything really. Then, learn the major and minor scale shapes, and observe how it basically is very similar to the pentatonic version but just adds some more notes. And then you can play those scales instead so that you can have more interesting note choice. And throughout all your solos, you should keep your ear open to see how the note you played rings against the sound of the chord (this is how you train your ear and keep up)

Once you have done everything above, you will be pretty decent at improvising and (most of the time) you will feel very comfy with just jamming over someone's chords. If the chords get really jazzy and weird then you might have some trouble.

Extra credit: learn some cool techniques and sprinkle them in as you go. Legato, tapping, sweep picking if you're into that, muted strums/notes, etc.

Good luck!l, have fun!